Problem: As Will is stuck in the Upside Down, he can still communicate with his mom, Joyce, through the Christmas lights (he can turn them on and off with his mind). He can't directly tell his mom where he is, because the monster that took him to the Upside Down will know and relocate him. 

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Thus, he came up with a puzzle to tell his mom his coordinates. His coordinates are the answer to the following problem.

A string consisting only of parentheses ('(' and ')') is called a bracket sequence. Some bracket sequence are called correct bracket sequences. More formally:

  * Empty string is a correct bracket sequence. 
  * if s is a correct bracket sequence, then (s) is also a correct bracket sequence. 
  * if s and t are correct bracket sequences, then st (concatenation of s and t) is also a correct bracket sequence. 



A string consisting of parentheses and question marks ('?') is called pretty if and only if there's a way to replace each question mark with either '(' or ')' such that the resulting string is a non-empty correct bracket sequence.

Will gave his mom a string s consisting of parentheses and question marks (using Morse code through the lights) and his coordinates are the number of pairs of integers (l, r) such that 1 ≤ l ≤ r ≤ |s| and the string slsl + 1... sr is pretty, where si is i-th character of s.

Joyce doesn't know anything about bracket sequences, so she asked for your help.

Input

The first and only line of input contains string s, consisting only of characters '(', ')' and '?' (2 ≤ |s| ≤ 5000).

Output

Print the answer to Will's puzzle in the first and only line of output.

Examples

Input

((?))


Output

4


Input

??()??


Output

7

Note

For the first sample testcase, the pretty substrings of s are:

  1. "(?" which can be transformed to "()". 
  2. "?)" which can be transformed to "()". 
  3. "((?)" which can be transformed to "(())". 
  4. "(?))" which can be transformed to "(())". 



For the second sample testcase, the pretty substrings of s are:

  1. "??" which can be transformed to "()". 
  2. "()". 
  3. "??()" which can be transformed to "()()". 
  4. "?()?" which can be transformed to "(())". 
  5. "??" which can be transformed to "()". 
  6. "()??" which can be transformed to "()()". 
  7. "??()??" which can be transformed to "()()()". 

Solution (in JAVA):

Solution:

import sun.reflect.generics.tree.Tree;

import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.util.Map.Entry;

public class Template {

    class Edge{
        int to;
        int num;
        Edge(int to, int num){
            this.to = to;
            this.num = num;
        }
    }

    class Vertex implements Comparable<Vertex>{
        int ind;
        int dist;
        int num;
        Vertex(int ind, int dist, int num){
            this.ind = ind;
            this.dist = dist;
            this.num = num;
        }

        @Override
        public int compareTo(Vertex o) {
            return Integer.compare(this.dist, o.dist);
        }
    }
    String fileName = "";
    TreeSet<Integer>[] nums = new TreeSet[46];
    int MODULO = 1000*1000*1000+7;
    void solve() throws IOException {
        char[] s = readString().toCharArray();
        int n = s.length;
        int ans = 0;
        for(int i=0; i<n; ++i){
            int q = 0;
            int b = 0;
            int q1 = 0;
            for(int j=i; j<n; ++j){
                if(s[j] == '(') b++;
                if(s[j] == ')') b--;
                if(s[j] == '?') q++;
                if(b<0 && q == 0 && q1 == 0){
                    break;
                }
                if(b<0 && q>0) {
                    q--;
                    b++;
                }
                if(b<0 && q1>0) {
                    q1--;
                    q++;
                    b++;
                }
                if(b>0 && s[j] == '?'){
                    q1++;
                    q--;
                    b--;
                }
                if((j-i)%2 == 1){
                    //out.println(i+1+" "+(j+1)+" "+q+" "+b);
                    if(b == 0 && q%2 == 0){
                        ans++;
                        //out.println(i+1+" "+(j+1) +"!!!!!");
                    }
                }
            }
        }
        out.println(ans);
    }

    ////////////////////////////////////////////////////////////
    class Pair{
        int num;
        int val;
        Pair(int num, int val ){
            this.num = num;
            this.val = val;
        }
    }
    class SegmentTree {
        int[] t;
        int[] nums;
        SegmentTree(int[] a) {
            int n = a.length - 1;
            t = new int[n * 4];
            nums = new int[n*4];
            build(a, 1, 1, n);
        }
        Pair max1;
        Pair max2;
        void build(int[] a, int v, int tl, int tr) {
            if (tl == tr) {
                t[v] = a[tl];
                nums[v] = tl;
                return;
            }

            int mid = (tr + tl) / 2;

            build(a, 2 * v, tl, mid);
            build(a, 2 * v + 1, mid + 1, tr);

            t[v] = Math.max(t[2 * v], t[2 * v + 1]);
            if(t[v] == t[2*v]){
                nums[v] = nums[2*v];
            }else{
                nums[v] = nums[2*v+1];
            }
        }

        void update(int v, int tl, int tr, int pos, int value) {
            if (tl == tr) {
                t[v] = value;
                return;
            }

            int mid = (tl + tr) / 2;

            if (pos <= mid) {
                update(2 * v, tl, mid, pos, value);
            } else {
                update(2 * v + 1, mid + 1, tr, pos, value);
            }

            t[v] = Math.max(t[2 * v], t[2 * v + 1]);
            if(t[v] == t[2*v]){
                nums[v] = nums[2*v];
            }else{
                nums[v] = nums[2*v+1];
            }
        }

        Pair getMax(int v, int tl, int tr, int l, int r) {
            if (l > r) {
                return new Pair(-1,-1000 * 1000);
            }
            if (tl == tr) {
                return new Pair(nums[v],t[v]);
            }

            if (l == tl && r == tr) {
                return new Pair(nums[v],t[v]);
            }

            int mid = (tl + tr) / 2;

            max1 = getMax(2 * v, tl, mid, l, Math.min(mid, r));
            max2 = getMax(2 * v + 1, mid + 1, tr, Math.max(mid + 1, l), r);

            int max = Math.max(max1.val, max2.val);
            if(max1.val == max){
                return max1;
            }else{
                return max2;
            }
        }
    }
    class Fenwik {
        long[] t;
        int length;

        Fenwik(int[] a) {
            length = a.length + 100;
            t = new long[length];

            for (int i = 0; i < a.length; ++i) {
                inc(i, a[i]);
            }
        }

        void inc(int ind, int delta) {
            for (; ind < length; ind = ind | (ind + 1)) {
                t[ind] += delta;
            }
        }

        long getSum(int r) {
            long sum = 0;
            for (; r >= 0; r = (r & (r + 1)) - 1) {
                sum += t[r];
            }
            return sum;
        }
    }
    int gcd(int a, int b){
        return b == 0 ? a : gcd(b, a%b);
    }

    long binPow(long a, long b, long m) {
        if (b == 0) {
            return 1;
        }
        if (b % 2 == 1) {
            return ((a % m) * (binPow(a, b - 1, m) % m)) % m;
        } else {
            long c = binPow(a, b / 2, m);
            return (c * c) % m;
        }

    }

    public static void main(String[] args) throws NumberFormatException, IOException {
        // TODO Auto-generated method stub
        new Template().run();
    }

    void run() throws NumberFormatException, IOException {
        solve();
        out.close();
    };

    BufferedReader in;
    PrintWriter out;

    StringTokenizer tok;
    String delim = " ";
    Random rnd = new Random();

    Template() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            if (fileName.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new PrintWriter(fileName + ".out");
            }

        }
        tok = new StringTokenizer("");
    }

    String readLine() throws IOException {
        return in.readLine();
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) {
                return null;
            }

            tok = new StringTokenizer(nextLine);
        }
        return tok.nextToken();
    }

    int readInt() throws NumberFormatException, IOException {
        return Integer.parseInt(readString());
    }
   byte readByte() throws NumberFormatException, IOException {
        return Byte.parseByte(readString());
    }
    int[] readIntArray (int n) throws NumberFormatException, IOException {
        int[] a = new int[n];
        for(int i=0; i<n; ++i){
            a[i] = readInt();
        }
        return a;
    }
    long readLong() throws NumberFormatException, IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(readString());
    }
}